# Multipole cut-off¶

The scattering properties of each particle are represented by its T-matrix $$T_{plm,p'l'm'}$$ where $$plm$$ and $$p'l'm'$$ are the multipole polarization, degree and order of the scattered and incoming field, respectively, see sections 3.3 and 2.3.2 of [Egel 2018]. In practice, the T-matrix is truncated at some multipole degree $$l_{max} \ge 1$$ and order $$0 \le m_{max} \le l_{max}$$ to obtain a finite system of linear equations.

Specify the cut-off parameters for each particle like this:

large_sphere = smuthi.particles.Sphere( ...
l_max=10,
m_max=10,
...)

small_sphere = smuthi.particles.Sphere( ...
l_max=3,
m_max=3,
...)


In general, we can say:

• Large particles require higher multipole orders than small particles.
• Particles very close to each other, very close to an interface or very close to a point dipole source require higher multipole orders than those that stand freely.
• Larger multipole cutoff parameters imply better accuracy, but also a quickly growing numerical effort.
• When simulating flat particles near planar interfaces, the multipole truncation should be chosen with regard to the Sommerfeld integral truncation. See [Egel et al. 2017].

Literature offers various rules of thumb for the selection of the multipole truncation in the case of spherical particles, see for example [Neves 2012] or [Wiscombe 1980].

Otherwise, you can use Smuthi’s built-in automatic parameter selection feature to estimate a suitable multipole truncation, see section on Automatic parameter selection.